2009 Rv Em P1

RIVER VALLEY HIGH SCHOOL 2009 PRELIMINARY EXAMINATION SECONDARY FOUR CANDIDATE NAME CLASS

4

INDEX NUMBER

___________________________________________________________________________

MATHEMATICS

4016/01

Paper 1

15 September 2009 2 hours

Candidates answer on the Question Paper.

___________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your class, index number and name on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. Calculators should be used where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142, unless the question requires the answer in terms of . At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

For Examiner’s Use

2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

2 Mathematical Formulae Compound interest Total amount = P( 1 +

r n ) 100

Measuration Curved surface area of a cone = rl Surface area of a sphere = 4r2 1 Volume of a cone = r2h 3 4 Volume of a sphere = r3 3 1 Area of triangle ABC = ab sin C 2

Arc length = r, where  is in radians 1 Sector area = r2, where  is in radians 2

Trigonometry a b c = = sin A sin B sin C

a2 = b2 + c2  2bc cos A

Statistics Mean =

Standard deviation =

2009 RVHS Preliminary Examination

 fx f  fx 2   fx    f f 

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2

O Level Mathematics (4016) P1

3 Answer all the questions. 1

Evaluate (a)

5.23 , 23.8  0.693

(b)

(8.96  10 6 )  ( 2.13  10 3 ) .

[Leave both your answers in standard form.]

Answer (a) …………………….………[1] (b) .……………………………[1] _________________________________________________________________________ 2

The pie chart shows how 120 students come to school. Find

car xo

(a)

the value of x,

(b)

the number of children who take

MRT

walk

xo

30o

bus to school,

cycle 2xo bus

Answer (a) x =………………………..….….[1] (b) .…………………….……......….[1] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

4

3

 3  (a) Simplify    2x 

3

(b) Given that 313  81  3 2 k , find the value of k

Answer (a)………………………………[1] (b) k = …………………………[1] ___________________________________________________________________________ 4

The time in Auckland is 4 hours ahead of Singapore. (a) Mr Yeo in Auckland calls his wife on her mobile phone at 13 38 Auckland time. Find the time in Singapore when Mrs Yeo receives the call. (b) They spoke briefly for 8 minutes before Mrs Yeo's mobile phone runs out of battery. She rushes home by bus, taking 1 hour 23 minutes, and calls her husband immediately. Find the time in Auckland when Mr Yeo gets the call.

Answer (a)………………………………[1] (b)………………………………[1] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

5 5

(a) A dealer sold a camera for $184. She made a profit of 15%. Calculate the cost price of the camera. (b) The selling price of a camera decreases from $560 to $480 during a sale. Calculate the percentage reduction in the selling price of the camera.

Answer (a) $ …………………..………. [1] (b) ......................................... % [1] ___________________________________________________________________________ 6 A A C 1414cm cm

D

B B

O

In the diagram, OAB is a quadrant of a circle, with a radius of 14cm. OB is the diameter 22 of a semicircle. Take  to be , calculate the total length of curves ODB and ACB. 7

Answer …..……………………..…… cm [2]

2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

6 7

The population of a city is 1.2  107. There are 8.0  10 6 senior citizens. The rest are young citizens. (a) What fraction of the population are senior citizens? (b) Find the number of young citizens, leaving your answer in standard form.

Answer (a)……………………..………. [1] (b) ...............................................[1] ___________________________________________________________________________ 8

The sketch represents the graph of y = mx + c. (a) Write down the value of c. (b) Find the value of m.

Answer (a) c =…………………..………. [1] (b) m =..........................................[1] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

7

P

9

B 41

A

C

40

Q

ABC is a triangle in which BAC = 90, AC = 40 cm and BC = 41 cm. The line AC is produced to Q. (a) Showing your working clearly, explain why AB = 9 cm. (b) Express as a fraction (i) tan BCA, (ii) cos BCQ.

[1]

Answer (b)(i) tan BCA = ……..………. [1] (b)(ii) cos BCQ =.......................[1] ___________________________________________________________________________ 10 For Valentine’s Day, a gift shop offers two types of packages consisting of roses, chocolates and candies. The matrices show the two types of packages and the cost of each rose, chocolate and candy. Roses Chocolates Candies Package A   Package B 

3

3

5

6

9

8

  

$ Rose

 1.2    Chocolate  0.5  Candy  0.3 

 1.2   3 3 5    0.5  (a) Find   6 9 8    0.3 

(b) Explain what your answer to (a) represent.

Answer (a)……………………..………. [2] (b) ............................................................................................................................................ .....................................................................................................................................[1] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

8 11

B

A



C

(a) On the Venn diagram above and shade the region that represents (A  B)  C’. (b) Given that  ={ x : x is a positive integer }, A = { 1, 2, 3, 4, 5, 6 }, B = { x : x is a multiple of 3, 3 < x  18 }, find n ( A’  B ).

[1]

Answer (b) n ( A’  B ) =………………...……… [2] ___________________________________________________________________________ 12 Given that

r2

3r  4T , express T in terms of r. 3T

Answer T = ……………………..………. [3] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

9 13 It is given that y varies inversely as x and y = 20 when x = 40. (a) Find an expression for the relationship between y and x. (b) If x increases by 50%, find the percentage change in y.

Answer (a)………………………………[1] (b)………………………………[2] ___________________________________________________________________________ 14

The dot diagram shows the number of pets kept by a group of students in a class. Find (a) the mode, (b) the median, (c) the percentage of students that have at least 3 pets,

Answer (a)………………………………[1] (b)………………………………[1] (c)………………………….. % [1] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

10 15 (a) Factorise completely 3 px  6qx  8qy  4 py . (b) Simplify 16 x 2  9  ( 4 x  3) 2

Answer (a)…………………….…………………………[2] (b)……………………………………….………[2] _______________________________________________________________________ 16 (a) Each interior angle of a regular polygon is eight times the corresponding exterior angle. Find the number of sides of the polygon. (b) A regular polygon has an interior angle of 140o. Calculate the number of sides of the polygon.

Answer (a)………………………..sides [2] (b)………………………..sides [2] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

11 17 (a) Given that three school bells ring at intervals of 25 minutes, 30 minutes and 1 hour respectively, calculate the next time they will ring together if they first ring together at 7.45 am. (b) Express the numbers 480 and 576 as the products of their prime factors. Find the smallest positive integer value of n for which 480n is a multiple of 576.

Answer (a)…………………….……….…[2] (b) 480 = ...………………………[1] 576 =…………………………[1] n = ………………………...[1] ___________________________________________________________________________ 18 (a) Find the largest integer k which satisfies k  2  4  5  k  . (b) Solve the simultaneous equations 5 x  2 y  13, 2 x  3 y  3.

Answer (a) k =……………………..…………. [2] (b) x = ....................., y = .....................[3] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

12 19 Two spherical containers A and B used for storing chemicals has a capacity of 80cm3 and 270cm3 respectively. The curve surface area of container A is given as 90cm2. (a) Find, in its simplest integer form, the ratio of the radius of the container A to the radius of the container B. (b) Calculate the surface area of container B. (c) A manufacturer charges $20 to paint container A. Find the cost of painting the container B.

Answer (a) Ratio =

……….. : ………..[1]

(b) …………………………cm2 [2] (c) $ ……………………………[2] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

13 20 P

Q

6n

V U

S

4m

R

T

PQRS is a parallelogram such that SR = 4m, SP = 6n. The line PT cuts RQ at U. It is 1 also given that RU = RQ. 3 (a) Express the following vectors in terms of m and n:  (i) RU

(ii)

 QU ,

(iii) PU ,  3 4 (b) V is a point on QT such that UV = 1 m + n, find SU and explain why S, U and 5 5 V are collinear points.

 Answer (a)(i) RU =…………..……………..…. [1] 

(ii) QU = …………………………….[1]

 (iii) PU = …………………………….[1] (b) ................................................................................................................................................ ...................................................................................................................................................... ...............................................................................................................................................[2] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

14 21 (a) (i) Sketch the graph of y  x(7  2 x) . (ii)Write down the equation of the line of symmetry of y  x(7  2 x) .

y Y

O

x

X

[2]

Answer (a)(ii )…………………………… [1]

(b) (i) Sketch the graph of

y  ( x  3) 2  1 .

(ii) Write down the coordinates of the minimum point of the curve.

y Y

O

x

X

[2] Answer (b)(ii ) (….…… , .……… ) [1]

2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

15 22 The diagram below is the speed-time graph of a lorry. The lorry starts from rest and steadily accelerates to a speed of 15m/s in 10 seconds. Its speed then remains constant 3 for some time before it steadily decreases at m/s 2 until it stops. The whole journey 4 takes one minute. (a) Given that the speed after x seconds is v m/s, express v in terms of x. (b) For how long does the lorry travel at the maximum speed ? (c) Calculate the total distance travelled by the lorry during this 1 minute. V m/s

15

v

0

x

10

60

t(s)

Answer (a) v = ….………………………[2] (b)……………………..…..… s [2] (c)…………………………. . m [2] 2009 RVHS Preliminary Examination

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O Level Mathematics (4016) P1

16 23

The diagram below shows the map of a triangular field ABC. The scale of the map is unknown. The bearing of C from A is 090o and D is a point on the side AB. (a) A point E lies on the angle bisector of BAC and is such that area of ∆ADC = area of ∆AEC. Locate and label the position of point E in the diagram, showing your method of construction clearly. (b) A point F is due south of A and is such that F is equidistant from B and C. Locate and label the point F in the diagram. Write down the bearing of C from F. (c) The actual distance of C from A is 172 m. Make use of this information to find an estimation for the actual area of ∆ABC in m2. B

D

×

North

A

C [3]

Answer (b) Bearing of C from F =…….….… [1] (c) 2009 RVHS Preliminary Examination

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…………………...……….…m2 [2] O Level Mathematics (4016) P1